A particular uranium alloy has a density of 18.75 g/cm3. Please answer the following questions below, providing the explanation to your answers. a. What volume is occupied by a critical mass of 49 kg of this alloy? b. The critical mass can be decreased to 16 kg if the alloy is surrounded by a layer of natural uranium (which acts as a neutron reflector). What is the volume of such smaller mass? Compare your answers to the approximate volumes of a baseball, a volleyball, and a basketball.

Comparison:

Explanation:

To find the volumes of the two samples of uranium alloy, you must use the formula of density:

a) Critical mass of 49 kg

First, notice that 18.75g/cm³ is the same that 18.75 kg/dm³ (to convert from grams to kg you must divide by 1,000, and to convert from cm³ to dm³ you must divide by 1,000; thus, dividing both numerator an denominator by the same number leaves the fraction unchanged).

Now you can compute:

You can convert to cm³ multiplying by 1,000cm³/dm³.

Thus, volume = 2,600 cm³.

b) Critical mass = 16 kg

Volume = 850cm³

Compare with approximate volumes of a baseball, a volleyball, and a basketball:

You can calculate those volumes by using the formula for the volume of a sphere:

For the baseball: radius ≈ 3.75cm

For the basketball radius ≈ 12.0 cm

Thus, the comparison of the volumes is:

Baseball < Crittical mass 16 kg of Uranium 16 kg < Critical mass 49 kg of Uranium  < Basketball

< > according to newton's third law of motion, forces always act in equal but opposite pairs. another way of saying this is for every action, there is an equal but opposite reaction.< >